Quantifying the performance of multi-pulse quantum sensing

The quality of a quantum operation determines the performance of quantum information processing, such as the sensitivity of quantum sensing. Different from the fidelity of quantum operation in quantum computation, we present an effective function to evaluate the performance and diagnose the imperfection of operations in multi-pulse based quantum sensing. The evaluation function directly links the realistic sensitivity with intrinsic sensitivity in a simple way. Moreover, guided by this evaluation function, we optimize a composite pulse sequence for high sensitivity nitrogen-vacancycenter based magnetometry against spectrum inhomogeneities and control errors to improve the signal-to-noise ratio of nanoscale nuclear magnetic resonance by 1 order of magnitude. It marks an important step towards quantitative quantum sensing with imperfect quantum control in practical applications.